“Why should I?” she says. “Why would I want to shake that amazing lady I played for 11 years?” Well, “Cheers” to that!

That beloved sitcom ran from 1982-1993 and has been in reruns ever since, much to the relief of those who need a late-night laugh. Not only did the show launch the careers of Ted Danson, Woody Harrelson and Kirstie Alley, but it snagged Perlman four Emmys as Carla Tortelli, the feisty, unfiltered barmaid who squawked like the Brooklynite Perlman is. Born in Coney Island, raised in Bensonhurst, she found her calling at a middle-school talent show when she sang and played the bongos like Ricky Ricardo, and was thrilled to make people laugh.

“Carla was allowed to really, really hate people,” Perlman tells The Post, in a surprisingly soft, very un-Carla-like voice, minus the barmaid’s big trashy earrings. (Perlman says she has them all in a box in her garage in Los Angeles.) “I loved playing the bad guy!”

For now, she’s playing someone entirely different: the well-meaning foster mother of a difficult girl in David Rabe’s drama “Good for Otto,” which opens off-Broadway Thursday night. As it happens, the 69-year-old has long worked with the Children’s Action Network, helping find permanent homes for foster children.

She has three children of her own, now grown, with Danny DeVito. The two met in 1971 at an off-Broadway play called “The Shrinking Bride.” Perlman had come to watch a girlfriend in the show, but she couldn’t take her eyes off DeVito, who played, as she recalls it, “a demented stableboy.” For her, at least, it seemed to be love at first sight.

“I had to meet him immediately,” she says. “I asked my friend if he had a girlfriend and she said no.” They went out to dinner afterward and, Perlman says, “I came on to him big time!” A few weeks later, she left Brooklyn and moved into his Manhattan apartment.

“I thought I hit the big time,” she says. “It was always my goal to live in Manhattan. I never thought of going to LA!”

But TV beckoned and a few years later, there they were. Soon, DeVito was starring as the dyspeptic dispatcher on “Taxi,” where Perlman had a recurring role as his sweet-natured girlfriend, Zena. (In 1982, toward the end of the “Taxi” run, they wed in real life.)

Then came “Cheers.” Not only did Perlman find herself with a new family of actors and writers, but her own family — her writer sister, Heide Perlman and their father, Phil — got involved, too. He played a barfly named Phil.

“After a while, he started getting some lines,” she says. “I got to pour a glass of water over his head. I think I maybe cracked an egg on it, too. I can’t remember.”

She fondly recalls the show’s kindly, dim-witted Coach, played by Nicholas Colasanto. When the actor died, the show’s producers and writers — whom she says knew he was terminally ill and uninsurable, but hired him anyway — gave Coach a loving send-off.

“Woody [Harrelson] took over for him and he had that same feeling of total honesty,” she says, “and he was so charismatic and cute!”

After “Cheers” ended, Perlman went on to movies (“Matilda”), plays (Broadway’s “The Tale of the Allergist’s Wife”) and TV (“The Mindy Project” and “Kirstie,” with former castmate Alley, among them). She spends most of her time in Los Angeles with her rescue dog, Zorro, but keeps a place in Chelsea, too — mostly to be near her actress daughter, Lucy. She and DeVito separated last year and, after a brief reunion, are apart again.

“We’ve been together a very long time, so there’s a lot of love and history,” she says. “We agree on enough things, so why [ruin] that with the yucky things that come with a divorce?”